关键词: Hf$_{0.5}$Zr$_{0.5}$O$_{2}$, orthorhombic phase, ferroelectric films, phase stability, thickness-dependent, ternary phase diagrams

Abstract: Hafnia-based ferroelectric materials, like Hf$_{0.5}$Zr$_{0.5}$O$_{2}$ (HZO), have received tremendous attention owing to their potentials for building ultra-thin ferroelectric devices. The orthorhombic(O)-phase of HZO is ferroelectric but metastable in its bulk form under ambient conditions, which poses a considerable challenge to maintaining the operation performance of HZO-based ferroelectric devices. Here, we theoretically addressed this issue that provides parameter spaces for stabilizing the O-phase of HZO thin-films under various conditions. Three mechanisms were found to be capable of lowering the relative energy of the O-phase, namely, more significant surface-bulk portion of (111) surfaces, compressive $c$-axis strain, and positive electric fields. Considering these mechanisms, we plotted two ternary phase diagrams for HZO thin-films where the strain was applied along the in-plane uniaxial and biaxial, respectively. These diagrams indicate the O-phase could be stabilized by solely shrinking the film-thickness below 12.26 nm, ascribed to its lower surface energies. All these results shed considerable light on designing more robust and higher-performance ferroelectric devices.

Key words: Hf$_{0.5}$Zr$_{0.5}$O$_{2}$, orthorhombic phase, ferroelectric films, phase stability, thickness-dependent, ternary phase diagrams